Lorentz factor via speed
========================

The *Lorentz factor* (also called the *gamma factor*) expresses how time intervals,
lengths, and other physical quantities transform for a body while it moves.

**Notation:**

#. :math:`c` (:code:`c`) is :attr:`~symplyphysics.quantities.speed_of_light`

**Conditions:**

#. The speed is less than speed of light.
#. Special-relativistic effects only (flat space-time, no gravity).

**Links:**

#. `Wikipedia – Definition <https://en.wikipedia.org/wiki/Lorentz_factor#Definition>`__

.. py:currentmodule:: symplyphysics.definitions.lorentz_factor_via_speed

.. py:data:: lorentz_factor

    :attr:`~symplyphysics.symbols.relativistic_mechanics.lorentz_factor` of the body.

Symbol:
    :code:`gamma`

Latex:
    :math:`\gamma`

Dimension:
    :code:`dimensionless`


.. py:data:: speed

    :attr:`~symplyphysics.symbols.classical_mechanics.speed` of the body.

Symbol:
    :code:`v`

Latex:
    :math:`v`

Dimension:
    :code:`velocity`


.. py:data:: definition

    :code:`gamma = 1 / sqrt(1 - v^2 / c^2)`


    Latex:
        .. math::
            \gamma = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}